Minimum average variance estimation (MAVE, Xia et al: 2002) is an effective dimension reduction method. It requires no strong probabilistic assumptions on the predictors, and can consistently estimate the central mean subspace. It is applicable to a wide range of models, including time series.
However, the least squares criterion used in MAVE will lose its effciency when the error is not normally distributed. In this article, we propose an adaptive MAVE which can be adaptive to different error distributions. We show that the proposed estimate has the same convergence rate as the original MAVE. An EM algorithm is proposed to implement the new adaptive MAVE. Using both simulation studies and a real data analysis, we demonstrate the superior finite sample performance of the proposed approach over the existing least squares
based MAVE when the error distribution is non-normal and comparable performance when the error is normal.